100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Summary Calculus gr 12 IEB & GDE notes $6.82   Add to cart
Quickly navigate to
Preview
  2.  
  3. 12th Grade
  4.  
  5. Mathematics

Summary

Summary Calculus gr 12 IEB & GDE notes

 26 views  0 purchase
  • Course
  • Mathematics
  • Institution
  • 12th Grade

Detailed notes of the Grade 12 Calculus section Including: Discontinuities Limits (examples included) Steps on differentiation using first principles Rules for differentiation Tangents to a curve Cubic functions Graph interpretation Curve sketching Optimisation (4 pages of examp...

[Show more]

Preview 2 out of 12  pages

Document information

  • June 4, 2022
  • 12
  • 2020/2021
  • Summary

Subjects

  • mathematics
  • math
  • ieb
  • ieb notes
  • calculus
  • calculus notes
  • summaries
  • paper 1
  • paper 2
  • math paper 1
  • math paper 2
  • gde
  • dbe
  • matric
  • gr 12
  • grade 12
  • gr 12 maths
  • maths
  • gr 12 math
  • notes

Written for

  • 12th Grade
  • Mathematics
  • 200
All documents for this subject (411)

Seller

avatar-seller
erinswanepoel

Reviews received

Content preview

Calculus

, lim


Differential Calculus
x -> 0

lim
h -> 0




Enables us to:
Work out the gradient at a point on a graph Sketch cubic graphs
Discontinuities
lim f(x) exists if xlim f(x) = xlim f(x)
Two types of discontinuities in graphs x -> a -> a- -> a+


Removable discontinuity Jump discontinuity Piecewise/split function




2 3




/
1 2


1 -1 1
-1


lim f (x) = b
lim f(x) = 3 lim- f(x) = 2
x -> a

lim lim the limit as x tends
x -> 1+ f(x) = 2 x -> 1 - f(x) = 2 to a is equal to b x -> 1+ x -> 1


f(1) ≠ 2, the limit exists Limit only exists if lim f(x) ≠ lim f(x)
x -> 1- x -> 1+
lim as x -> a from left & right
the limit does not exist
x -> 1 f(x) = 2 but f(1) ≠1 f (x) tends to same value b


Limits
Determine the following limits: - Sub x value into the function
3x
lim (x + 5) lim lim - if 0/0 factorise and cancel!
x -> -4 x -> 3 (2/3x +3) x -> 0 x
3x
lim - don’t drop lim until sub x in
= -4 + 5 = 2/3(3) + 3 x -> 0 x

=1 =5 =3

x2- 1 x-4
lim lim x2- 4 lim 2x2- x lim
x -> 1 x-1 x -> 2 x2- 3x + 2 x -> 0 x x -> 4 x-2
lim (x - 1) (x + 1) lim (x + 2) (x - 2) lim x(2x -1) lim ( x - 2) ( x + 2)
x -> 1 (x - 1) x -> 2 (x - 1) (x - 2) x -> 0 x x -> 4 ( x - 2)
lim (x + 1) lim (x + 2) lim (2x - 1) lim ( x + 2)
x -> 1 x -> 2 (x - 1) x -> 0 x -> 4


=1+1 = 4/2 = -1 =4
=2 =2

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller erinswanepoel. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $6.82. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

72349 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$6.82
  • (0)
  Add to cart